From 60 to 90 it increases in the ratio of 10 to 17. From 90 to 180 it increases in the ratio of 75 to 100.
When the small globe was only the diameter of the other, the density of the small globe increased.
In the large globe of 8 inches, the density was nothing to the 4th or 5th degrees from the point of contact. It then increased rapidly, and from 30' to 130° it was al most uniform.
From these experiments we may conclude in general, that the more the globes are unequal, the more does the density of the small globe vary from the point of contact to 180°, and the more does the distribution of the elec tric matter on the great globe approach to uniformity, in creasing rapidly from the point of contact, where it is nothing, to the 7th or 8th degree from this point, and being uniform over all the rest of its surface.
In order to compare these experiments with the theory of the distribution of electricity after the law of the inverse duplicate ratio of the distance, Coulomb found it necessary to make some subsidiary experi ments, which are well worthy of being detailed as gene ral facts.
Exp. 1. Having placed between two electrified globes of the same size, a small globe, whose diameter was less than the sixth part of the diameter of either, so that all the three were in contact, he found that the small globe, when presented to a very sensible electrometer, gave no signs of electricity, and that however small the middle globe was it possessed no negative electricity.
Exp. 2. When three equal globes, two inches in di ameter, were placed in contact in a right line, one of the globes, supported by the pincers Fig. 3, was placed suc cessively between the two others, and on each side of both. In these different positions it was presented to the great torsion balance, and the quantity of electricity be ing measured, it was found, that when it was placed in the middle it took more electricity than when it was placed at either of the sides, in the ratio of 100 to 134. This result is the mean of the experiments made after equal intervals, for the purpose of correcting the error arising from the dissipations.
Exp. 3. Hitherto we have seen that when two globes were in contact, the density at the point of contact and in the adjacent parts was nothing, and was never negative when the two globes were positively electrified. But the
moment the two globes are separated, then if one of the globes is smaller than the other, and if the distance of the two globes is not great, the point of the little globe which was in contact with the great globe, will become negative, till they are separated to a certain distance. At this distance, the electricity is again nothing, and, by increasing the distance, the same point becomes after wards positive.
Exp. 4. Having insulated a globe of 11 inches dia meter, and also another globe of a smaller size, electri fy them and bring them into contact. Let the small globe be then taken to a different distance, and, by means of a very small ball of lead suspended by gum lac, or by means of a circle of gilt paper, touch the small globe at the point where it touched the great globe, and examine in the small torsion balance the nature of the electricity of that point.
When the large globe is 11 inches in diameter, and the small one 8 inches, and both positively electrified, the point of contact of the great globe is always posi tively electrified, whatever be the distance between the two. The point of contact of the small globe, however, will be negatively electrified, till the distance of the two is one inch. At this distance it becomes nothing, and be yond it its electricity is positive.
If the small globe is only 4 inches in diameter, the other remaining the same, the phenomena are precisely the same ; but they take place at 2 inches instead of I inch.
When the small globe is only 2 inches in diameter, or less than 2 inches, the other remaining the same, the same phenomena take place, but at the distance of 2 inch es and 5 lines.
The following Table contains some curious results, sheaving the relation between the mean density D of the largest of two globes after its separation from the small globe, to the density d of the point of the small globe, with which it was in contact, Il being the radius of the large globe, and r that of the small one.